We prove the $H^{infty}$ well-posedness of the forward Cauchy problem for a $Psi$-do differential operator $P$ of order $mgeq 2$ with Log-Lipschitz continuous symbol in the time variable. The characteristic roots $lambda_k$ of $P$ are distinct and satisfy the necessary Lax-Mizohata condition Im$lambda_kgeq 0$. The Log-Lipschitz regularity has been tested as the optimal one for $H^{infty}$ well-posedness in the case of second order hyperbolic operators. Our main aim is to present a simple proof which needs only a little of the basic calculus of standard $Psi$-do differential operators.

The Cauchy problem for a class of Kovalevskian pseudo-differential operators.

CICOGNANI, MASSIMO;AGLIARDI, ROSSELLA
2004

Abstract

We prove the $H^{infty}$ well-posedness of the forward Cauchy problem for a $Psi$-do differential operator $P$ of order $mgeq 2$ with Log-Lipschitz continuous symbol in the time variable. The characteristic roots $lambda_k$ of $P$ are distinct and satisfy the necessary Lax-Mizohata condition Im$lambda_kgeq 0$. The Log-Lipschitz regularity has been tested as the optimal one for $H^{infty}$ well-posedness in the case of second order hyperbolic operators. Our main aim is to present a simple proof which needs only a little of the basic calculus of standard $Psi$-do differential operators.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/4460
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